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What does the sigma symbol mean in math?

Anonymous Fri 01 Apr 15:55:17 2022 No.14354824 View Reply Original Report

Quoted By: >>14354885 >>14355139

I am taking general chemistry/organic chemistry and I frankly don't remember anything about math beyond simple arithmetic like addition, subtraction, dividing and multiplying.
First of all, what does the equation in pic rel mean? Can someone give me an example I can write down in my notebook so I can understand it?
Second, how can I get a bootcamp/crash course on essential math for college (chemistry/pharmacy) without studying shit I don't need?

Anonymous

Anonymous Fri 01 Apr 2022 15:55:52 No.14354825 Report

Quoted By:

What does the cursive "E" mean?

Anonymous

Anonymous Fri 01 Apr 2022 15:56:13 No.14354827 Report

Quoted By: >>14354831 >>14354835

It means sum

Anonymous

Anonymous Fri 01 Apr 2022 15:58:25 No.14354831 Report

Quoted By: >>14356659

>>14354827
I googled that, but can someone show me how it's summed?
Like 3-4 solved examples of this equation?

Anonymous

Anonymous Fri 01 Apr 2022 15:59:26 No.14354835 Report

Quoted By: >>14354840

>>14354827

is it:
(isotope mass of element1xfractional isotope abundance) + (isotope mass of element2xfractional isotope abundance) + (isotope mass of element3xfractional isotope abundance) + (isotope mass of element4xfractional isotope abundance)

Anonymous

Anonymous Fri 01 Apr 2022 16:00:48 No.14354840 Report

Quoted By: >>14354852

>>14354835
yes

Anonymous

Anonymous Fri 01 Apr 2022 16:04:17 No.14354852 Report

Quoted By:

>>14354840
thank you mathbro

Anonymous

Anonymous Fri 01 Apr 2022 16:14:37 No.14354885 Report

Quoted By:

>>14354824
it means sigma male grindset <img class="xae" data-xae width="29" height="32" src="https://s.4cdn.org/image/emotes/7a95728b_Gigachad.png">;

Anonymous

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Anonymous Fri 01 Apr 2022 17:06:44 No.14355139 Report

Quoted By:

>>14354824
>filename
Based
Also there's the Pi operator, I don't think you'll see it but it means product

Anonymous

Anonymous Fri 01 Apr 2022 22:19:29 No.14356132 Report

Quoted By: >>14356142

It means you summation.
$\sum_{i = 0}^k 1 = 1 + 1 + 1... + 1$ k times

$\sum_{i = 0}^k i = 0 + 1 + 2 + 3 + ... + k$

$\sum_{i \in I = \{1,2,3\}} v_i = v_1 + v_2 + v_3$

$\sum_{i = 0}^{\infty} i = 0 + 1 + 2 + 3 + ...$

$\sum_{x \in \mathbb{N}} x = \sum_{x = 0}^{\infty} x$

The product is the same thing, instead of a plus you use multiplication. This notation is generalized to any type of operation, ie, just make the symbol big and write it the same way.
$\prod_{x = 0}^k x = 1 \cdot 2 \cdot 3 \cdot ... \cdot n$

$\bigcup_{X \subseteq S} X = X_1 \cup X_2 \cup X_3 ...$

$\sum_{x \in \text{isotope}} (m_x p_x) = m_1p_1 + m_2p_2 + ... + m_n$

Anonymous

Anonymous Fri 01 Apr 2022 22:21:45 No.14356142 Report

Quoted By:

>>14356132
Whoops, fucked up, product, starts with 0 and there is a m_np_n at the end of the sum.

Anonymous

Anonymous Sat 02 Apr 2022 01:36:14 No.14356659 Report

Quoted By:

>>14354831
hydrogen has 3 isotopes, 1u 2u and 3u so it's atomic weight is the sum of masses of these 3 isotopes multiplied by their share in the population of hydrogen. 1u*0,979+2u*0,02+3u*0,001 = 1,002

Anonymous

Anonymous Sat 02 Apr 2022 04:40:44 No.14357014 Report

Quoted By:

>sigma symbol mean in math
Uppercase: summation or an alphabet
Lowercase: standard deviation

Anonymous

Anonymous Sat 02 Apr 2022 04:44:58 No.14357022 Report

Quoted By: >>14357109

$ \delta \, \epsilon \left ( 0,1 \right ) \\ \displaystyle \prod_{k=0}^{n} \left ( 1 + \delta ^{2^{k}} \right ) = (1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\ (1- \delta) \prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right ) = (1- \delta)(1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\ = (1- \delta ^{2})(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\ = (1- \delta ^{4})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) = (1- \delta ^{2^{n}})(1+ \delta ^{2^{n}}) = 1- \delta ^{2^{n+1}} \\ \\ \boxed{(\delta ^{2^n})^2 = \delta ^{2 \cdot 2^n}=\delta^{2^{n+1}}} \\ \displaystyle \prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right ) = \dfrac{1- \delta^{2^{n+1}}}{1- \delta} \\ \displaystyle \lim_{n \to \infty} \prod_{k=0}^{n} \left (1+ \delta ^{2^{k}} \right ) = \lim_{n \to \infty} \dfrac{1- \delta^{2^{n+1}}}{1- \delta} = \dfrac{1}{1- \delta} $

Anonymous

Anonymous Sat 02 Apr 2022 05:49:05 No.14357109 Report

Quoted By:

>>14357022
For a second I thought you were doing a delta-epsilon limit. Just use $\in$

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